what is normal reaction? is it always equal to weight(mg) of an object?

If not, 1.when it is not equal? & 2.how much is it different cases?

what is normal reaction for a vehicle performing circular motion along concave bridge & convex bridge?(explain with the help of centripetal force, weight "mg".)

Asked by shubham.padamwar.3 | 16th Dec, 2014, 10:49: PM

Expert Answer:


When two objects are in contact with each other, normal reaction appears. Consider an object placed on a surface. Normal reaction is the reaction force experienced by the object in a direction perpendicular to the surface, when the object is pressed against the surface.This prevents the object from falling from the surface and is the only force that the surface exerts on the object in the absence of frictional forces.It always points outwards and perpendicular to the surface of contact. It is called the normal reaction since it acts at a 90° angle with respect to the surface.

Normal reaction is not always equal to the weight of the object. It is due to this fact that the force of friction is not related to the weight of the body but it is related to the normal reaction. Normal reaction is equal to the weight of the object if the normal force and the weight are the only forces on the object, which often happens.

When an object is placed on an inclined plane, inclined at an angle with the horizontal, the force acting on the body will be the force of gravity acting downwards.This can be resolved into its two components , mg sin θ and mg cos θ as shown.

As the body slides down the plane, the net force acting can be written as:

R -mg cos θ = 0

i.e. R =mg cos θ and not equal to mg (weight). It will vary with the angle of inclination θ.

Similarly when an object placed on a horizontal surface is pulled by a force F, the perpendicular component of force acts vertically upwards and the weight of the object acting downwards  is balanced by the perpendicular component of force Fsin θ along with normal reaction(R) .

In this case:

mg =R+Fsinθ.

i.e. R =mg -Fsinθ

This indicates that the normal reaction decreases when we pull an object.


For a car moving over a convex bridge or concave bridge , the centripetal force required for the circular motion is provided by the normal reaction R of the bridge acting upwards and the weight of the car mg acting downwards.

In a convex bridge the central portion bulges upwards, 

So centripetal force (mv2)/ r = mg - R

Therefore the normal reaction at the maximum height, R = mg - (mv2)/ r

In a concave bridge the central portion goes downwards,

So centripetal force (mv2)/ r =R - mg

Therefore the normal reaction at the minimum height, R = (mv2) / r + mg

Answered by Jyothi Nair | 18th Dec, 2014, 11:11: PM